Acyclic and k-distance coloring of the grid

In this paper, we give a relatively simple though very efficient way to color the d-dimensional grid G(n₁,n₂,…,n_d) (with n_i vertices in each dimension 1?i?d), for two different types of vertex colorings: (1) acyclic coloring of graphs, in which we color the vertices such that (i) no two neighbors are assigned the same color and (ii) for any two colors i and j, the subgraph induced by the vertices colored i or j is acyclic; and (2) k-distance coloring of graphs, in which every vertex must be colored in such a way that two vertices lying at distance less than or equal to k must be assigned different colors. The minimum number of colors needed to acyclically color (respectively k-distance color) a graph G is called acyclic chromatic number of G (respectively k-distance chromatic number), and denoted a(G) (respectively χ_k(G)).The method we propose for coloring the d-dimensional grid in those two variants relies on the representation of the vertices of G_d(n₁,…,n_d) thanks to its coordinates in each dimension; this gives us upper bounds on a(G_d(n₁,…,n_d)) and χ_k(G_d(n₁,…,n_d)).We also give lower bounds on a(G_d(n₁,…,n_d)) and χ_k(G_d(n₁,…,n_d)). In particular, we give a lower bound on a(G) for any graph G; surprisingly, as far as we know this result was never mentioned before. Applied to the d-dimensional grid G_d(n₁,…,n_d), the lower and upper bounds for a(G_d(n₁,…,n_d)) match (and thus give an optimal result) when the lengths in each dimension are “sufficiently large” (more precisely, if ). If this is not the case, then these bounds differ by an additive constant at most equal to . Concerning χ_k(G_d(n₁,…,n_d)), we give exact results on its value for (1) k=2 and any d?1, and (2) d=2 and any k?1.In the case of acyclic coloring, we also apply our results to hypercubes of dimension d, H_d, which are a particular case of G_d(n₁,…,n_d) in which there are only 2 vertices in each dimension. In that case, the bounds we obtain differ by a multiplicative constant equal to 2.     

Influence of the fermentation yeast strain on the composition of wine spirits

Fifteen indigenous strains of Saccharomyces cerevisiae, differentiated by their genetic polymorphism, were compared in standard conditions for their respective ability to produce volatile compounds during the alcoholic fermentation of grape must. The results were processed using analysis of variance and of principal components. They exhibited significant differences between strains, in particular for the higher alcohols, fatty acid esters, acetates or acetaldehyde. On the basis of their analytical profile, five strains were selected and compared on the pilot scale. Overall, the pilot results confirmed laboratory findings. As the strain effect appears to be determinant on the aromatic composition of wine spirits, a programme of selection based on both intraspecific molecular characterisation and chromatographic analysis is carried out to obtain specific yeast strains for high-quality spirits.     

Sensitivity of roots to errors in the coefficient of polynomialsobtained by frequency-domain estimation methods

Although the roots of a polynomial of high order are extremely sensitive to perturbations in its coefficients, experience has demonstrated that frequency-domain estimation techniques succeed in the determination of accurate poles and zeros, even in the case of high-order transfer function models. The authors prove that this is due to the correlations among the estimated coefficients. When the result of a measurement is a set of correlated values, they conclude that it is not justifiable to use the standard deviation to determine the number of significant digits. Additional digits have to be considered in order to maintain the information enclosed in the correlations     

Intra-macrophage lipid particles collected by bronchoalveolar lavage: incidence and diagnostic value

This study aimed to determine the incidence and diagnostic value of fat-laden alveolar macrophages obtained by bronchoalveolar lavage (BAL). In 128 patients, including 66 patients admitted for multiple trauma, 158 BAL were carried out. However, 41 BAL from 32 patients were excluded because of poor quality of samples (not enough macrophages, too many ciliated cells, or haemorrhage). All the patients were intubated and mechanically ventilated, having pulmonary infiltrates on the chest film. BAL samples were examined after staining with oil-red-O. They were considered to be positive when more than 5% of alveolar macrophages contained fat droplets. Among them 14 out of 47 patients (30%) without multiple trauma were positive; 7/14 had never been given any intravenous lipid infusion, and 5/14 had aspiration pneumonia (as opposed to 3/32 patients with negative BAL). Further 27 patients out of the 49 (55%) with multiple trauma were positive. Among them 10/49 had clinical evidence of fat embolism, however, only 7/10 had positive samples. All these last ten patients had been given intravenous lipid infusions. The rate of positive alveolar macrophages was correlated neither with the plasma triglyceride concentration, nor the Fracture Index Score, nor the delay between the end of the lipid infusion and the BAL. There was no significant difference in PaO2/FIO2 ratio between the patients with positive and negative BAL. Positive BAL was significantly associated with lipid infusions. The data therefore suggest that the presence of fat-laden alveolar macrophages are associated with various pathological pulmonary conditions, particularly aspiration pneumonia and lipid infusions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Identification of linear systems captured in a feedback loop

The identification of model parameters using measured input-output data from linear systems operating in a closed loop is discussed. A frequency-domain maximum likelihood estimator which takes into account the correlation between the input and output disturbances is presented. Its properties are analyzed and illustrated by simulation examples and real measurements     

Etude de l'alliage mulberry [U-7,5 Nb-2,5 Zr (% ponderaux)]. diagramme de transformation en refroidissement continu-structures et proprietes mecaniques

We have studied by dilatometry, microscopy, X-ray and electron diffraction, the phase transformations generated by controlled cooling from 900° C of the “Mulberry” alloy (U-7.5 wt%Zr). For slow cooling rates, three types of decomposition of the 7 phase appear successively: (i) Between 600°C and 550°C, grain boundaries and inclusion serve as nucleation sites for a cellular reaction, $\text{γ→α+γ}$; (ii) between 550°C and 400°C, a continuous transformation of the matrix generates an a phase in the form of Widmanstätten plates, and (iii) below 400°C, the γ phase gives rise to an α″ phase which has an ultrafine structure only imperfectly resolved by TEM. On rapid cooling, a tetragonal phase, γ₀, appears. Quenching generates the γ_S phase derived from γ, with a structure crystallizing in 143m which has been described by YakeL The various methods of investigation used have allowed us to obtain heating and cooling curves of the alloy and thus to determine phase fields. In general terms, the structures formed are similar to those obtained by isothermal annealing below 600° C. Only the γ_S phase has useful mechanical properties, notably good ductibility. The other phases are characterised by extreme brittleness.     

Photocontrolled Hierarchical Self‐Assembly of Anisotropic Micropatterns of Nanofibers onto Isotropic Surfaces

Hierarchical self‐assembly is achieved using a visible light triggered photoreaction. A pro‐gelator, α‐diketone‐2,3‐didecyloxyanthracene, is photoconverted into a low molecular weight gelator, 2,3‐didecyloxyanthracene (DDOA), that self‐assembles into nanofibers. Spatial confinement and patterns of these nanofibers onto a surface are achieved by localizing initial nucleation with a focused laser and photogenerate subsequent fiber growth with the laser or gentler wide‐field irradiation. Remarkably, collective growth of nanofibers results in anisotropic micropatterns with orientation factors (OF) reaching 79%, resulting in collective emission of linearly polarized light. The OF, distance of collective growth and fiber density, are controlled by the photoirradiation conditions and the balance of interactions between DDOA aggregates and the glass surface. An unprecedented juxtaposition of orthogonally oriented nanofiber patterns on an isotropic surface is achieved with individual control of the fibers' main direction. In perspective, this photochemical method can be extended to a large variety of self‐assembling molecules.